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Algo/CM/CM du 04 octobre.md
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@ -29,3 +29,29 @@ That an consistency, because the two `nth`axioms are contradictory
The completeness is when we have enough axioms for our abstract type
To use partial operations we have to create some preconditions
```
Types
vector
Uses
integer, element, boolean
Operations
Vect: integer x integer -> vector /* internal operation */
Modify : vector x integer x element -> vector /*internal operation*/
Nth: vector x integer -> element /* Observers */
isint: vector x integer -> boolean
Lowerlimit: vector -> integer /* Observers */
Upperlimit: vector -> integer /* Observers */
Preconditions
nth(v,i) is-defined-iaoi lowerlimit(v) =< (i) =< upperlimit(v) & isinit(v,i) = true
Axioms
lowerlimit(v) =< i =< upperlimit(v) -> nth(modify(v,i,e), i) = e
lowerlimit(v) =< i =< upperlimit(v) & lowerlimit(v) =< j =< upperlimit(v) & i≠j -> nth(modifiy(v,i,e), j) = nth(v,j)
isinit(vect(i,j),k)= false
lowerlimit(v) =< i =< upperlimit(v) -> isinit(modifiy(v,i,e),i)= true
... (all the other axioms)
```
Here, `nth`is a partial operation and `isinit` is a auxiliary operation